Regular polygon → Infinite polygon → Circle-Original Sky Butterfly's Mathematics

 Regular polygon = isosceles triangleⁿ, d = polygon, π = circle

 

Square = isosceles triangle × 4 → Regular pentagon = isosceles triangle × 5 → Regular hexagon = isosceles triangle × 6 → Regular heptagon = isosceles triangle × 7 → Regular octagon = isosceles triangle × 8 → … … → isosceles triangleⁿ = infinite polygon=circle (π)

 

Triangle 2 division⩟½=sin(30½)×2

Regular Polygons and Angles

 

Square (D4) → 360/D4 = A90 → Isosceles Triangle A90, C45, C45

 

 

*Triangle 2 division

Calculate the area of ​​the isosceles triangle abc when r1.

Angle, A+B+90=180, B+A½=C

 

ab1, ac1, ad=cosA(sinB), bd=sinA

Area=ab×bd(sinA)×½

ab×tanA=bd(sinA), bd×tanB=bd(sinB)

 

π3.1415926535897932384626433832795

Regular 1024-sided polygon 3.1415914215111999739979717637408

Regular 1536-sided polygon 3.1415921059992715505447766406101

*square

Isosceles n = regular polygon d

 

a is one side of the regular polygon, tanA is the height ratio, n is the number of sides of the regular polygon, 1/4 is base a ½ × triangle area ratio ½ = 1/4

 

a² is base a × h (base a ½ × tanA)

When a b = 1,

1×(1/2×tan 45)×½×4

 

*Regular pentagon

 

*Regular pentagon angle 5/360=72, (180-72)×½=54

 

Area of ​​a regular pentagon when side a3

 

Since the height h = 3/2 × tan 54, multiplying by the base a3 × ½ gives the area of ​​an isosceles triangle, which corresponds to multiplying by the number of sides of an isosceles regular pentagon.

 

a3 × (3/2 × tan 54) × ½ × 5 = Area of ​​a regular pentagon

 

A 72-degree angle is 18 degrees.

A relative angle of 18 degrees is 72 degrees.

 

 infinite regular polygon = circle

infinite regular polygon (infinite isosceles triangle)

Isosceles triangles are divided into two equal parts. When all of the isosceles triangles divided into infinity are combined, they become infinitely polygons, and a circle is established.